Related papers: Ray Effect Mitigation for the Discrete Ordinates M…
Solving the radiation transport equation is a challenging task, due to the high dimensionality of the solution's phase space. The commonly used discrete ordinates (S$_N$) method suffers from ray effects which result from a break in…
The commonly used velocity discretization for simulating the radiative transport equation (RTE) is the discrete ordinates method (DOM). One of the long-standing drawbacks of DOM is the phenomenon known as the ray effect. Due to the high…
The Discrete Ordinates Method (DOM) is the most widely used velocity discretization method for simulating the radiative transport equation. However, the ray effect is a long-standing drawback of DOM. In benchmark tests that exhibit the ray…
The Discrete Ordinates Method (DOM) is widely used for velocity discretization in radiative transport simulations. However, DOM tends to exhibit the ray effect when the velocity discretization is not sufficiently refined, a limitation that…
A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
Dynamic scattering remains a significant challenge to the practical deployment of anti-scattering imaging. Existing methods, such as transmission matrix measurements, iterative wavefront shaping, and optical phase conjugation, depend on a…
The quasi-random discrete ordinates method (QRDOM) is here proposed for the approximation of transport problems. Its central idea is to explore a quasi Monte Carlo integration within the classical source iteration technique. It preserves…
Rendering highly scattering participating media using brute force path tracing is a challenge. The diffusion approximation reduces the problem to solving a simple linear partial differential equation. Flux-limited diffusion introduces…
The radiative transfer equation (RTE) arises in many different areas of science and engineering. In this paper, we propose and investigate a discrete-ordinate discontinuous-streamline diffusion (DODSD) method for solving the RTE, which is a…
Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical…
Understanding how laser light scatters from realistic mirror surfaces is crucial for the design, com- missioning and operation of precision interferometers, such as the current and next generation of gravitational-wave detectors. Numerical…
The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and…
Scattering by an isolated defect embedded in a dielectric medium of two dimensional periodicity is of interest in many sub-fields of electrodynamics. Present approaches to compute this scattering rely either on the Born approximation and…
In this work we investigate the use of the Analytical Discrete Ordinates (ADO) method when solving the spectral approximation of the nonclassical transport equation. The spectral approximation is a recently developed method based on the…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…
We solve the radiative transfer equation (RTE) in anisotropically scattering media as an infinite series. Each series term represents a distinct number of scattering events, with analytical solutions derived for zero and single scattering.…
An antireflective coating presenting a continuous refractive index gradient is theoretically better than its discrete counterpart because it can give rise to a perfect broadband transparency. This kind of surface treatment can be obtained…
In this paper, we propose a novel machine learning-based method to solve the acoustic scattering problem in unbounded domain. We first employ the Dirichlet-to-Neumann (DtN) operator to truncate the physically unbounded domain into a…
This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the…
Some novel numerical approaches to solving direct and inverse obstacle scattering problems (IOSP) are presented. Scattering by finite obstacles and by periodic structures is considered. The emphasis for solving direct scattering problem is…